Question

A stock just paid a dividend of $1.17. The dividend is expected to grow at 21.41% for three years and then grow at 4.10% thereafter. The required return on the stock is 14.60%. What is the value of the stock?

A stock just paid a dividend of $1.81. The dividend is expected to grow at 24.24% for five years and then grow at 3.81% thereafter. The required return on the stock is 12.06%. What is the value of the stock?

Answer 1

Requirement 1:

D₀ = $ 1.17

D₁= $ 1.17 + $ 1.17 x 0.2141 = $ 1.17 + $ 0.250497 = $ 1.420497

D₂= $ 1.420497 + $ 1.420497 x 0.2141 = $ 1.420497 + $ 0.3041284077 = $ 1.7246254077

D₃ = $ 1.7246254077 + $ 1.7246254077 x 0.2141 = $ 1.7246254077 + $ 0.36924229978857

= $ 2.09386770748857

D₄ = $ 2.09386770748857 + $ 2.09386770748857 x 0.041

     = $ 2.09386770748857 + $ 0.0858485760070314 = $ 2.1797162834956014

As per dividend discount model, price of stock on year 3^rd,

P₃ = D₄ / (r – g)

D₄ = Dividend on year 4 = $ 2.1797162834956014

r = Required return = 14.60 % or 0.146

g = Constant growth rate = 4.10 % or 0.041

P₃ = $ 2.1797162834956014/ (0.146 – 0.041)

    = $ 2.1797162834956014/0.105

     = $ 20.7592026999581

Stock price today = D₁/(1+r) + D₂/(1+r)₂ + D₃/(1+r)³+ P₃ /(1+r)³

= $ 1.420497/ (1+0.146) + $ 1.7246254077/ (1+0.146)² + $ 2.09386770748857/ (1+0.146)³+

$ 20.7592026999581/ (1+0.146)³

= $ 1.420497/ (1.146) + $ 1.7246254077/ (1.146)² + $ 2.09386770748857/ (1.146)³+

$ 20.7592026999581/ (1.146)³

= $ 1.420497/1.146 + $ 1.7246254077/ 1.313316 + $ 2.09386770748857/ 1.505060136 +

$ 20.7592026999581/ 1.505060136

= $ 1.23952617801047 + $ 1.31318388544722 + $ 1.39121863466097 + $ 13.7929390350673

= $ 17.73686773318596 or $ 17.74

Value of stock is $ 17.74

Requirement 2:

D₀ = $ 1.81

D₁= $ 1.81 + $ 1.81 x 0.2424 = $ 1.81 + $ 0.438744 = $ 2.248744

D₂= $ 2.248744 + $ 2.248744 x 0.2424 = $ 2.248744 + $ 0.5450955456 = $ 2.7938395456

D₃ = $ 2.7938395456+ $ 2.7938395456 x 0.2424 = $ 2.7938395456 + $ 0.67722670585344

= $ 3.47106625145344

D₄ = $ 3.47106625145344 + $ 3.47106625145344 x 0.2424

     = $ 3.47106625145344 + $ 0.841386459352314 = $ 4.31245271080576

D₅ = $ 4.31245271080576 + $ 4.31245271080576 x 0.2424

     = $ 4.31245271080576 + $ 1.04533853709932 = $ 5.35779124790508

D₆ = $ 5.35779124790508 + $ 5.35779124790508 x 0.0381

     = $ 5.35779124790508 + $ 0.20413184654518 = $ 5.56192309445026

As per dividend discount model, price of stock on year 5^th

P₅ = D₆ / (r – g)

D₆ = Dividend on year 6 = $ 5.56192309445026

r = Required return = 12.06 % or 0.1206

g = Constant growth rate = 3.81 % or 0.0381

P₅ = $ 5.56192309445026/ (0.1206 – 0.0381)

    = $ 5.56192309445026/0.0825

     = $ 67.4172496297001

Stock price today = D₁/(1+r) + D₂/(1+r)₂ + D₃/(1+r)³+ D₄/(1+r)⁴+ D₅/(1+r)⁵+P₅ /(1+r)⁵

= $ 2.248744/ (1+0.1206) + $ 2.7938395456/ (1+0.1206)² + $ 3.47106625145344/ (1+0. 1206)³+

+ $ 4.31245271080576/ (1+0. 1206)⁴ + $ 5.35779124790508/ (1+0.1206)⁵ + $ 67.4172496297001/ (1+0.1206)⁵

= $ 2.248744/ (1.1206) + $ 2.7938395456/ (1.1206)² + $ 3.47106625145344/ (1.1206)³+ $ 4.31245271080576/ (1.1206)⁴ + $ 5.35779124790508/ (1.1206)⁵ + $ 67.4172496297001/ (1.1206)⁵

= $ 2.248744/1.1206 + $ 2.7938395456/ 1.255744+ $ 3.47106625145344/ 1.407187129816

$ 4.31245271080576/ 1.57689389767181 + $ 5.35779124790508/ 1.76706730173103 + $ 67.4172496297001/1.76706730173103

= $ 2.00673210779939 + $ 2.2248473770569 + $ 2.46666998148804 + $ 2.7347767133685

+ $ 3.03202444109319 + $ 38.1520554218041

= $ 50.61710604261012 or $ 50.62

Value of stock is $ 50.62